$G$-designs for the connected triangular bicyclic graphs with nine edges
نویسندگان
1 Department of Mathematics, Iowa State University, 411 Morrill Road, Ames, USA
2 Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, USA
3 School of Mathematics, University of Minnesota, 127 Vincent Hall 206 Church St. SE, Minneapolis, USA
4 Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN
5 Department of Mathematics and Statistics University of Minnesota Duluth 1117 University Dr. Duluth, MN 55812-3000 USA
doi
10.22108/toc.2024.140831.2156چکیده
A $G$-design of order $n$ is a decomposition of the complete graph $K_n$ into isomorphic copies of $G$. We show that if $G$ is a connected bicyclic graph with nine edges containing two triangles, a $G$-design of order $n$ exists whenever $n \equiv 0,1 \pmod{18}$.
